Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#123 | C2 |
| prime radical | #11745299 | C2 |
| hypercenter | #123 | D29 |
| hypocenter | C29 | #551 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#123 | C2 | semidirect |
| 3. #11745298 | C2 | semidirect |
| 4. C4×C22⋊D29 | C2 | semidirect |
| 5. #11745258 | C2 | semidirect |
| 6. #11745254 | C2 | semidirect |
| 7. #11745245 | C2 | semidirect |
| 8. C22⋊C4×D29 | C2 | semidirect |
| 9. #11745241 | C2 | semidirect |
| 12. C22×C4×C29 | C22 | semidirect |
| 16. C2×Dic58 | C22 | semidirect |
| 17. C4⋊C4×C29 | C22 | semidirect |
| 19. C22⋊C4×C29 | C22 | semidirect |
| 22. C22⋊Dic29 | C22 | semidirect |
| 26. C4⋊Dic29 | C22 | semidirect |
| 27. #90779 | C22 | semidirect |
| 28. #90779 | C22 | semidirect |
| 29. C4×Dic29 | C22 | semidirect |
| 30. C4×Dic29 | C22 | semidirect |
| 72. #123 | D29 | semidirect |
| 78. C29 | #551 | semidirect |
| 85. C22×C4 | C2×D29 | semidirect |
| 89. C4⋊C4 | C2×D29 | semidirect |
| 97. C22⋊C4 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#123 | 2 |
| #11745299 | 2 |
| #11745298 | 2 |
| C4×C22⋊D29 | 2 |
| #11745258 | 2 |
| #11745254 | 2 |
| #11745245 | 2 |
| C22⋊C4×D29 | 2 |
| #11745241 | 2 |
| #551 | 29 |